Field ionization in short and extremely intense laser pulses

Modern laser systems are able to generate short and intense laser pulses ionizing matter in the poorly explored barrier-suppression regime. Field ionization in this regime is studied analytically and numerically. For analytical studies, both the classical and the quantum approaches are used. Two approximations to solve the time-dependent Schr\"odinger equation are proposed: the free electron approximation, in which the atomic potential is neglected, and the motionless approximation, in which only the external field term is considered. In the motionless approximation, the ionization rate in extremely strong fields is derived. The approximations are applied to several model potentials and are verified using numeric simulations of the Schr\"odinger equation. A simple formula of the ionization rate both for the tunnel and the barrier-suppression regimes is proposed. The formula can be used, for example, in particle-in-cell codes for simulations of the interaction of extremely intense laser fields with matter.